Fascination is a slow waltz (“valse lente”), sometimes called Valse Tzigane.
Music by Fermo Dante Marchetti (Italian composer, born 1876, died 1940).
The original instrumental version was published in 1904 in Hamburg and Paris, for piano solo.
In 1905, lyrics in French were added by Maurice de Féraudy; the song was then performed by Paulette Darty, a French music-hall singer.
When WWI broke out in 1914, Fascination was already about a decade old. From what I could find:
There is no clear evidence that Fascination was written for WWI, or that it was particularly tied to wartime propaganda or battlefield culture in the early war years.
Because it was already well-known as a sentimental waltz, it may have been among the kinds of popular music enjoyed in salons, cafés, or via music-hall performances during that period (i.e. part of civilian/opera-house / café culture), rather than war-front songs.
The song’s content (lyrics) is romantic rather than martial, which suggests its purpose was entertainment, romantic sentiment, not patriotic or martial mobilization.
So, Fascination belongs more to the Belle Époque musical/salon culture, which carried over into WWI, but it was not composed for wartime or as a war song.
While Fascination was not specifically a WWI piece, its later popularity means people often associate or hear it in historical contexts:
It has been adapted in many languages, recorded by many artists.
It also appeared in films (e.g. Love in the Afternoon / Ariane (1957)), which revived its popularity.
Because it was well-known before WWI and was continued after, it helps illustrate how culture and popular music persisted through turbulent periods. Even if not overtly political, pieces like this shaped the emotional backdrop of the era (sentiments of nostalgia, romance, stability).